Context.M 87 is a giant
elliptical galaxy located in the centre of the Virgo cluster, which harbours a
supermassive black hole of mass 6.4 × 109M⊙,
whose activity is responsible for the extended (80 kpc) radio lobes that surround the
galaxy. The energy generated by matter falling onto the central black hole is ejected and
transferred to the intra-cluster medium via a relativistic jet and morphologically complex
systems of buoyant bubbles, which rise towards the edges of the extended halo.

Aims. To place constraints on past activity cycles of the active
nucleus, images of M 87 were produced at low radio frequencies never explored before at
these high spatial resolution and dynamic range. To disentangle different synchrotron
models and place constraints on source magnetic field, age and energetics, we also
performed a detailed spectral analysis of M 87 extended radio-halo.

Methods. We present the first observations made with the new
Low-Frequency Array (LOFAR) of M 87 at frequencies down to 20 MHz. Three observations were
conducted, at 15−30 MHz, 30−77 MHz and 116−162 MHz. We used these observations together
with archival data to produce a low-frequency spectral index map and to perform a spectral
analysis in the wide frequency range 30 MHz–10 GHz.

Results. We do not find any sign of new extended emissions; on the
contrary the source appears well confined by the high pressure of the intra-cluster
medium. A continuous injection of relativistic electrons is the model that best fits our
data, and provides a scenario in which the lobes are still supplied by fresh relativistic
particles from the active galactic nuclei. We suggest that the discrepancy between the
low-frequency radio-spectral slope in the core and in the halo implies a strong adiabatic
expansion of the plasma as soon as it leaves the core area. The extended halo has an
equipartition magnetic field strength of ≃10 μG, which increases to
≃13 μG in the zones where the particle flows are more active. The
continuous injection model for synchrotron ageing provides an age for the halo of
≃40 Myr, which in turn provides a jet kinetic power of
6−10 × 1044 erg s-1.